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Birational geometry of hypersurfaces : Gargnano del Garda, Italy, 2018 / Andreas Hochenegger, Manfred Lehn, Paolo Stellari, editors.

9783030186388 (electronic book)
3030186385 (electronic book)
9783030186371

Cham, Switzerland : Springer, 2019.

English

Chapters in English and French.

1 online resource (ix, 297 pages) : illustrations

10.1007/978-3-030-18638-8 doi
10.1007/978-3-030-18

QA471

516/.5

Originating from the School on Birational Geometry of Hypersurfaces, this volume focuses on the notion of (stable) rationality of projective varieties and, more specifically, hypersurfaces in projective spaces, and provides a large number of open questions, techniques and spectacular results. The aim of the school was to shed light on this vast area of research by concentrating on two main aspects: (1) Approaches focusing on (stable) rationality using deformation theory and Chow-theoretic tools like decomposition of the diagonal; (2) The connection between K3 surfaces, hyperkähler geometry and cubic fourfolds, which has both a Hodge-theoretic and a homological side. Featuring the beautiful lectures given at the school by Jean-Louis Colliot-Thélène, Daniel Huybrechts, Emanuele Macrì, and Claire Voisin, the volume also includes additional notes by János Kollár and an appendix by Andreas Hochenegger.

Includes bibliographical references.

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Online resource; title from PDF title page (SpringerLink, viewed October 16, 2019).

Lecture notes of the Unione Matematica Italiana ; 26.

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